U.S. patent number 4,991,934 [Application Number 07/392,428] was granted by the patent office on 1991-02-12 for varied space diffraction grating and in-focus monochromator.
Invention is credited to Michael C. Hettrick.
United States Patent |
4,991,934 |
Hettrick |
February 12, 1991 |
**Please see images for:
( Certificate of Correction ) ** |
Varied space diffraction grating and in-focus monochromator
Abstract
An optical system and method comprising a diffraction grating
which consists of diffracting elements spaced from one another by
unequal distances. Correction of residual defocusing in the image
produced by such a grating is accomplished by translating it along
its surface. As one embodiment, a monochromator is constructed on
which a self-focusing grating scans the value in wavelength which
is transmitted between fixed slits by rotation of the grating about
an axis fixed in space. Combined with a translation of the grating
along its surface, such a monochromator produces a symmetrical
image exactly in focus at the exit slit for all scanned
wavelengths.
Inventors: |
Hettrick; Michael C. (Berkeley,
CA) |
Family
ID: |
23550554 |
Appl.
No.: |
07/392,428 |
Filed: |
August 10, 1989 |
Current U.S.
Class: |
359/570; 356/328;
356/334; 359/572; 359/575 |
Current CPC
Class: |
G01J
3/06 (20130101); G01J 3/18 (20130101); G02B
5/1861 (20130101); G01J 3/1804 (20130101); G01J
2003/069 (20130101); G01J 2003/1847 (20130101); G01J
2003/1852 (20130101) |
Current International
Class: |
G01J
3/18 (20060101); G01J 3/00 (20060101); G01J
3/06 (20060101); G02B 5/18 (20060101); G01J
3/12 (20060101); G02B 005/18 () |
Field of
Search: |
;350/162.21,162.22,162.24,162.23,162R ;356/334,328 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
F M. Gerasimov et al., "Concave Diffraction Gratings with Variable
Spacing", Opt. & Spectrosc. (U.S.A.), vol. 28, No. 4, 1979, pp.
423-426. .
H. A. Rowland, "On Concave Gratings for Optical Purposes,", Phil.
Mag., vol. 16, 1883, pp. 197-210. .
T. Harada et al., "A Grazing Incidence Monochromator with a
Varied-Space Plane Grating for Symchrotron Radiation," SPIE vol.
350, 1984, pp. 114-118. .
G. Monk, "A Mounting for the Plane Grating," J. Opt. Soc. Am., vol.
17, 1928, pp. 358-364. .
T. Namioka, "Theory of the Concave Grating III, Seya-Namioka
Monochromator," J. Opt. Soc. Am., vol. 49, 1959, pp. 951-961. .
M. C. Hettrick et et al., "Stigmatic High Throughput Monochromator
for Soft X-Rays," Appl. Opt., vol. 25, 1986, pp. 4228-4231. .
M. C. Hettrick et et al., "Variable Line-Space Gratings: New
Designs for Use in Grazing Incidence Spectrometers," Appl. Opt.,
vol. 22, 1983, pp. 3921-3924. .
M. C. Hettrick, "High Resolution Gratings for the Soft X-Ray,"
Nucl. Instrum. Meth., vol. A-66, 1988, pp. 404-413. .
M. C. Hettrick et et al., "Resolving Power of 35,000 (5 mA) in the
Extreme Ultraviolet Employing a Grazing Incidence
Spectrometer,"Appl. Opt., vol. 27, 1988, pp. 200-202..
|
Primary Examiner: Arnold; Bruce Y.
Assistant Examiner: Ryan; J. P.
Claims
What is claimed is:
1. A grating which comprises:
a. a concave surface;
b. a plurality of substantially parallel diffracting elements
spaced from each other by unequal distances as projected upon a
chord of said concave surface, according to a density function;
c. an object point substantially fixed in space;
d. an image point substantially fixed in space;
e. a first path length equal to the distance which extends between
said fixed object point and a first one of said diffracting element
plus the distance which extends between said first diffracting
element and said fixed image point;
f. a second path length equal to the distance which extends between
said fixed object point and a second one of said differacted
element plus the distance which extends between said second
diffracting element and said fixed image point;
wherein the difference between said first and second path lengths
plus a distance equal to a non-zero integer times a chosen
wavelength times an integer equal to one plus the number of
diffracting elements intervening said first and said second
diffracting elements, defines a path-length error function, said
grating characterized in that said concave surface, density
function and said object and image points are chosen such that said
path-length error function when written as a sum of powers of said
chord distance between said first and said second diffracting
elements lacks both second and third power terms at more than one
distinct said chosen wavelength diffracted from said fixed object
to said fixed image, said distinct wavelengths being determined by
rotation of said grating about a fixed axis.
2. The grating of claim 1, in which said fixed axis is
substantially tangent to one of said parallel diffracting
elements.
3. The grating of claim 1, in which said concave surface is
substantially spherical and reflecting.
4. The grating of claim 3, in which said density function is
written as
where .sigma..sub.o, N.sub.2, N.sub.3, N.sub.4, etc. are constant
coefficients, where .sigma. is the said chord spacing between
neighboring said diffracting elements, and where w is the said
chord distance from a reference said diffracting element where said
chord is tangent to said spherical surface.
5. The grating of claim 4, in which
where subscripts 1 and 2 refer to the quantity as determined using
.alpha. and .beta. given by
.lambda..sub.1 and .lambda..sub.2 being two said distinct
wavelengths of choice, m being the spectral order, .theta. being an
angle of choice, .sigma..sub.o being a spacing of choice, and where
R is the radius of curvature of said spherical surface.
6. The grating of claim 1, in which said concave surface is a
spherical and reflecting.
7. The grating of claim 1, in which the angle subtended by lines
drawn from any said diffracting element to said fixed object and to
said fixed image, exceeds 140.degree..
8. The grating of claim 1, in which said distinct wavelengths are
electromagnetic wavelengths within the range 3-2500 .ANG..
9. An optical system comprising:
a. a granting which comprises a surface having substantially
parallel diffracting elements spaced from one another by unequal
distances as measured along a straight line tangent to the grating
surface at a point;
b. means for rotating said grating about an axis substantially
fixed in space;
c. means for translating said grating in a direction substantially
parallel to a tangent plane of said surface.
10. The optical system of claim 9, in which said surface is
concave.
11. The optical system of claim 10, in which said concave surface
is substantially spherical and reflecting.
12. The optical system of claim 10, in which said concave surface
is a spherical and reflecting.
13. The optical system of claim 9, in which said surface is
substantially planar.
14. The optical system of claim 13, used in combination with an
incident plane wave.
15. The optical system of claim 13, used in combination with a
virtual object, providing a converging wave to said grating.
16. The optical system of claim 9, in which said rotation axis is
substantially parallel to said diffracting elements.
17. The optical system of claim 9, in which said rotation axis lies
substantially on said surface of said grating.
18. The optical system of claim 9, employed in combination with a
source of radiation and a target means receiving said radiation,
said grating located between said source and said target means,
additionally comprising at least one optical element disposed in
the path of light which travels between said source and said target
means, said optical element arranged to cause said source radiation
to focus in a plane substantially parallel to said diffracting
elements.
19. The optical system of claim 18, in which said optical element
comprises a concave reflecting surface having a normal which lies
substantially within a plane which is parallel to a tangent of said
grating surface.
20. The optical system of claim 19, in which said concave
reflecting surface is a cylinder.
21. The optical system of claim 19, in which said concave
reflecting surface is a sphere, which additionally causes said
radiation to focus in the plane which is substantially
perpendicular to said diffracting elements.
22. The optical system of claim 18, in which said optical element
comprises a concave reflecting surface having a normal which lies
substantially within the same plane as a normal to the surface of
said grating.
23. The optical system of claim 22, in which said concave
reflecting surface is a cylinder.
24. The optical system of claim 22, in which said concave
reflecting surface is a sphere, which additionally focuses said
radiation in the plane which is substantially perpendicular to said
diffracting elements.
25. The optical system of claim 9, additionally comprising at least
one narrow opening, or slit, located at a position substantially
fixed in space, whereby said slit limits the passage of all but a
narrow band of wavelengths diffracted by said grating.
26. The optical system of claim 9 used in combination with
electromagnetic radiation having wavelengths in the range 3-2500
.ANG..
27. The optical system of claim 9, in which said means for rotating
said grating and said means for translating said grating are
mechanically coupled.
28. The optical system of claim 9, in which said means for rotating
said grating comprise a cam.
29. The optical system of claim 9, in which said means for
translating said grating comprise a cam.
30. The optical system of claim 9, wherein said means for rotating
said grating comprise a bar which translates with said grating.
31. The optical system of claim 30, further including a body which
translates in a linear direction, said body having a substantially
planar surface which is in contact with said bar, said planar
surface being inclined at a finite angle relative to said linear
direction.
32. The optical system of claim 9, employed in combination with a
source of radiation, additionally comprising an entrance slit and
at least one optical element disposed in the path of light which
travels between said source and said grating, said optical element
arranged to cause said radiation to be efficiently directed to and
transmitted through said entrance slit.
33. A method for aligning varied-space gratings in spectrometers
and monochromators comprising the steps of:
a. employing a grating having a surface which is not rotationally
symmetric about any line, and which comprises a plurality of
substantially parallel diffracting elements spaced from each other
by unequal distances as measured along a straight line tangent to
said grating surface at a point; and
b. translating said grating substantially along said surface and in
a direction substantially perpendicular to said diffracting
elements.
Description
BACKGROUND OF THE INVENTION
This invention relates to a novel optical system which has several
inherent advantages over existing monochromators employing
electromagnetic radiation and operating at grazing incidence.
Rowland (1883) was the first to design a self-focusing diffraction
grating, thereby constructed a reflection grating monochromator
consisting of a single element having useable efficiency. The
Rowland grating comprises grooves equally spaced along the chord of
a concave spherical surface. The spectral images are in focus along
a circle whose diameter equals the grating radius of curvature.
Monochromators based upon this design require effective movement of
at least one of the slits along the Rowland circle during the
wavelength scan.
To provide useable reflection efficiency for wavelengths shorter
than approximately 1000 .ANG., the grating is generally operated at
grazing incidence. In this application, designs based upon the
Rowland grating become increasingly cumbersome, due to the fact
that the Rowland circle must also lie at a grazing angle relative
to the light rays. Thus, the required slit movements become
enormous, resulting in complex mechanical designs and large vacuum
and mounting structures. In addition, optimal relaying and
refocusing of the light is obtained only if the attached target
chamber and/or light source chamber is moved in concert with the
slit(s). The expense and mechanical awkwardness of such systems
prohibits their widespread use as a practical method of achieving
high resolution.
Modern grazing incidence embodiments of the Rowland concept (e.g.
Brown et al, U.S. Pat. No. 4,398,823) have been adapted to use with
fixed beam directions, but only with the introduction of auxiliary
mirrors which must undergo complicated motions in concert with the
grating scan and translation of one slit along the beam direction.
Absent of such undesirable complications, a conventional concave
grating can simply be rotated about its pole to select the
wavelength diffracted between fixed slits, as demonstrated by the
Hettrick et al (1986) "high throughput monochromator." Due to a
drastic departure from the Rowland condition, such an optical
system is limited to low or moderate spectral resolution as
discussed by Hettrick (1988).
Recently, monochromators have been developed which employ
diffraction grating designs in which the grating surface comprises
groove elements which are spaced from one another by systematically
varying distances. Such monochromators can exhibit improved
performance compared to those which employ conventional equally
spaced gratings, due to the extra degree of freedom delivered by a
judicious choice of the variation in groove spacings. In this way,
aberrations in the image may be reduced or eliminated at one or
more wavelengths, resulting in higher spectral and/or spatial
resolution.
Prior art designs employing this idea have achieved wavelength
scanning in one of two ways, through either pure rotation of the
grating or through pure translation of the grating. At normal or
near normal incidence (e.g. Seya-Namioka mount), a given varied
spacing on a concave surface can maintain an improvement in the
resolution over a broad wavelength region as the grating is purely
rotated (Harada et al, U.S. Pat. No. 4,312,569). However, at
grazing incidence no net improvement is obtained in this manner.
Therefore, prior art grazing incidence varied-space designs which
scan wavelength through pure rotation of the grating have utilized
a plane (or large radius) grating in combination with an auxiliary
mirror. This mirror has either been flat and undergone a
complicated scanning motion (Harada et al, 1984) or be highly
figured to provide focusing in the dispersion direction of the
grating (Hettrick et al, U.S. Pat. No. 4,776,696; Hettrick 1988;
Hettrick et al 1988; Pouey, U.S. Pat. No. 4,241,999). Any such
auxiliary mirrors decrease the efficiency, add to the size and
expense of the resulting monochromator, and introduce additional
sources of fabrication and alignment errors. The method of pure
grating translation (Aspnes, U.S. Pat. No. 4,492,466) employs a
long cylindrical grating requiring a variation in groove spacing
which is at least as large as the wavelength region which may be
scanned, imposing a severe technical limitation on the grating
fabrication. In none of the above designs are the images perfectly
in focus at all scanned wavelengths, this condition being only
approximately met at a linearly increasing level of accuracy as the
numerical aperture is reduced.
A monochromator which employs a varied-space diffraction grating
which is self-focusing, requires only modest amounts of variation
in the groove spacings, produces spectral images which are in focus
at all scanned wavelengths, and operates at grazing incidence with
fixed slit positions and beam directions, would be a great advance
in the field of optics.
SUMMARY OF THE INVENTION
In accordance with the present invention, a novel and useful
optical system for a monochromator is provided.
The system of the present invention may utilize a diffraction
grating which focuses radiation from an entrance slit or other
source through an exit slit (or onto a target). The wavelength
transmitted through the exit slit is scanned by rotating the
surface of said grating about an axis fixed in space. The grating
surface comprises grooves whose spacings are unequal. At each
orientation of the grating corresponding to a particular scanned
wavelength, the grating is also translated in the direction of its
surface tangent. Given a sufficiently high degree of variation in
the groove spacing, this translation provides complete freedom to
bring each wavelength into an exact focus, even if both the
entrance slit and exit slit are fixed in position. Further, by
choosing the slit distances and groove spacing function
appropriately, higher order aberrations may also be eliminated at
several chosen discrete wavelenghts.
The novelty of this scheme can be appreciated from the fact that
such translation would have no effect upon the properties of a
conventional (equally-spaced) grating. As varied space gratings are
only presently becoming accepted as viable designs, the very
existence of this additional degree of freedom is not appreciated
in the prior art. Thus, the grating itself cannot be derived as
simply an aberration-corrected version which improves the
performance of a previously existing monochromator design. In
contrast, the Harada et al concave grating design is an improvement
over an equally-spaced grating when both are situated in a
Seya-Namioka mount (Namioka, 1959); while the Hettrick plane
grating design can be viewed as an improvement over an
equally-spaced grating when both are situated in a Monk-Gillieson
mount (Monk, 1928). However, the present invention is both that of
the grating and its mounting, which takes specific advantage of the
fundamental properties and practical limitations of varied
spacing.
When combined with a rotation which provides for broad wavelength
selection, the required amounts of space variation and translation
are easily within existing limits of grating manufacture and
mechanical design. Because the grating translates along its
surface, the fixed axis about which the grating rotates may always
intersect the grating surface at the same point in space, and thus
the direction of the (principal) ray which strikes this point is
fixed both incident and diffracted through the slits.
More than one such configuration may be placed in series, to form a
multiple grating monochromator having improved spectral resolution
(i.e. additive dispersion) or temporal resolution (i.e.
common-path-length).
Although not required in order to provide spectral resolution,
additional optics may be inserted in this optical design for the
purpose of focusing in the direction perpendicular to dispersion
(i.e. controlling or eliminating astigmatism).
It may be apparent that an improved optical system for a
monochromator has been described.
It is therefore an object of the present invention to provide an
optical system which possesses high efficiency due to the presence
of a minimum number of optical elements.
Another object of the present invention is to provide an optical
system which enables scanning over a broad range in wavelength.
Yet another object of the present invention is to provide an
optical system which is perfectly in focus at all scanned
wavelengths, providing high spectral resolution.
A further object of the present invention is to provide a
symmetrical image, which enables enhancement of the resolution
through modeling of the image profile.
Another object of the present invention is to provide an optical
system which employs slits (or object and image) which are fixed in
space.
Yet another object of the present invention is to provide an
optical system whose principal ray is fixed in direction both
incident to an exiting the slits (or object and image).
A further object of the present invention is to employ optical
surfaces which can be easily and inexpensively fabricated to
precise tolerances, enabling the practical realization of high
resolution.
Another object of the present invention is to provide a
monochromator consisting of a single optical element, thereby
allowing the construction of a compact and lightweight vacuum or
mounting structure which may be easily transported, or
inexpensively deployed in environments above the atmosphere.
The invention possesses other objects and advantages especially as
concerns particular characteristics and features thereof, which
will become apparent as the specification continues.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a side schematic view of the optical layout of the
present invention.
FIG. 2 is a top plan schematic view of the grating of the present
invention.
FIG. 3 is a sketch of the coordinate systems used for defining the
varied spacing before and after translation of the grating by an
amount .DELTA.w along a chord to its surface.
FIG. 4 is a set of graphs depicting the optical aberrations as
functions of scanned wavelength for a concave grating, employing
both the prior art and the present invention, and the grating
translation required in the present invention.
FIG. 5 is a front elevational view of the mechanical assembly of
the grating stage of the present invention.
FIG. 6 is a side elevational view in partial section generally
taken along the line 6--6 of FIG. 5.
FIG. 7 is a side detail view of a lead screw and inclined plane
pusher block arrangement in place of the wavelength cam shown in
FIG. 6.
Drawing referenced numerals:
10--optical system,
12--diffraction grating,
14--grating surface,
16--extended light source,
18--entrance slit,
20--incident principal ray,
22--pre-optic,
24--compact light source,
26--grating groove,
28--diffracted principal ray,
30--exit slit,
32--target,
34--grating rotation axis,
36--incident extremum ray,
38--diffracted extremum ray,
40--rotated grating surface (dashed) tangent line at rotation axis
34,
42--transverse positioning means for entrance slit,
44--transverse positioning means for exit slit,
46--optional orthogonal focusing mirror,
48--visible alignment source,
50--entrance grating aperture baffle,
52--grating holder,
54--grating set screws,
56--grating holder mounting bolts,
58--slide plate,
60--end plate,
61--end plate pivot clamps,
62--inner ways,
63--inner way mounting bolts,
64--outer ways,
65--outer way mounting bolts,
66--ball bearings,
68--grating translation cam,
70--grating translation cam contact ball,
72--grating translation bar,
74--translation bar extension spring,
76--extension spring pins,
77--lead screw,
78--wavelength drive cam,
79--inclined plane pusher block,
80--wavelength drive cam contact ball,
81--wavelength cam extension spring,
82--wavelength drive radius bar/end plate,
83--wavelength cam spring pins,
84--end plate flexural pivots,
85--alternate radius bar, oriented parallel to translation,
86--stationary support members,
87--support member pivot clamps,
88--base plate,
90--support members mounting bolts,
91--cam shaft,
92--cam shaft radial bearings,
93--anti-backlash worm gear,
94--worm,
95--drive shaft,
96--drive shaft radial/thrust bearings,
97--drive shaft retaining rings,
98--drive shaft leaf spring,
67--end plate/pivot mounting screws,
99--external rotation means,
100--prior art defocusing,
102--prior art coma,
104--prior art spherical aberration,
106--prior art grating translation (zero),
200--defocusing with no grating translation,
202--coma with no grating translation,
204--spherical aberration with no grating translation,
300--defocusing (zero) with grating translation,
302--coma with grating translation,
304--spherical aberration with grating translation,
306--required grating translation,
402--coma with grating translation and spherical term,
404--spherical aberration with translation and spherical term,
406--required grating translation with spherical term,
206--grating translation (zero) corresponding to curve 200.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Various aspects of the invention will evolve from the following
detailed description of the preferred embodiments thereof which
should be taken in conjunction with the hereinbefore described
drawings.
The optical layout of the invention as a whole is shown in FIG. 1
by referenced character 10. Optical system 10 includes as its key
element a diffraction grating 12, as shown in FIGS. 1 and 2. The
grating has a surface 14 which is reflective to the electromagnetic
radiation of interest which is emitted by an extended source 16 and
passes through an entrance slit 18 along a principal axis 20.
Pre-optics 22 may be inserted between a compact source 24 and the
entrance slit in order to efficiently direct the passage of such
light. The reflective surface of the grating is composed of a set
of minute grooves 26 which provides an interference pattern in the
reflected (i.e. diffracted) beam exiting the grating along a
principal axis 28. An exit slit 30 may be employed to allow passage
of an exceedingly narrow band of wavelengths .DELTA..lambda. to a
target or other detection means 32. In this manner, optical system
10 effectively transmits only a desired wavelength emitted by the
source, and hence performs the function of a monochromator.
To provide focusing in the direction of the grating grooves (i.e.
normal to dispersion), a mirror 46 may be interposed anywhere
between the light source 16 and the target 32. If the mirror is
cylindrical and oriented orthogonal to the grating surface, this
arrangement can greatly concentrate or collimate the image
intensity at the target (or any intermediate position) without
sacrifice of spectral resolution. However, an actual mirror will
possess slope errors (ripples, twisting, etc.) and other surface
irregularities which will distort the wavefront in the dispersion
direction of the grating. This will degrade the spectral resolution
unless the mirror is placed on the side of either slit opposite the
grating. If such a mirror is placed between the exit slit and the
target, then the focusing of light through the entrance slit by the
pre-mirror will also not degrade. In addition, a post-mirror (not
shown), similar in function to the pre-mirror, can be used to
further concentrate the image brightness by refocusing or
collimating the exit slit onto the target in the dispersion
direction.
To provide selection of the desired transmitted wavelength, the
grating is rotated about a fixed axis 34 so as to scan a continuous
band of wavelengths past the exit slit, as depicted in FIG. 1. To
maintain a fixed beam direction for principal light rays 20 and 28
which intersect at the grating center (or pole) w=0, the rotation
axis is preferred to pass through this pole. Given a constant
included angle, 2.theta., between the incident principal ray 20 and
diffracted principal ray 28, the required angle of incidence,
.alpha., and angle of diffraction, .beta., relative to the grating
surface normal are:
where .sigma..sub.o is the groove spacing at the pole, and m is the
spectral order.
Entrance slit 18 and exit slit 30 are ideally provided with
transverse positioning means 42 and 44, respectively. This enables
adjustment of the angle 2.theta. and thereby using equation (1)
provides an accurate absolute wavelength calibration. Such slit
assemblies may be Model VSA-300 available commercially from
Hettrick Scientific, Inc. Such alignment, and also the rotational
alignment of the slit length along the direction of the grating
grooves, may be facilitated by use of a visible alignment source 48
incident normally on the grating surface and diffracted through the
slits.
To minimize the optical aberrations, the spacings between the
grating grooves 26 are allowed to vary as a function of their
position, w, across the grating surface. Such a function may be
expressed in various ways, but for purposes of illustrating the
degree of aberration correction provided, it is written here as a
polynomial:
where N.sub.i are constant coefficients which determine the local
spacings between the centers of each groove, where i=2,3,4,
etc.
Given straight grooves, the error .DELTA.L in path length between
entrance and exit slit, and the resulting optical aberration
.DELTA..lambda. in wavelength for a non-principal ray 36 which
strikes aperture coordinate w (FIG. 1) is given to a good
approximation by:
and where R is the radius of curvature of the grating, r is the
length of principal ray 20 connecting the entrance slit and the
grating pole, and r' is the length of diffracted principal ray 28
connecting the grating pole and the exit slit.
The image at the transmitted wavelength is considered to be "in
focus" if F.sub.2 =0, and the image profile is to a first order of
approximation symmetrical if there is no coma (F.sub.3 =0). Given
the constraint of fixed entrance and exit slits, these two
conditions may both be honored at two wavelengths of choice,
.lambda..sub.1 and .lambda..sub.2, if the grating has a finite
radius and is simply rotated about its pole to select wavelength.
From equations 1-8, this solution leads to the following choice of
parameters: ##EQU2##
where subscripts 1 and 2 refer to the quantity as determined using
.alpha. and .beta. derived from equation (1) at the chosen
wavelengths .lambda..sub.1 and .lambda..sub.2, and where for
conciseness of equations (9) and (10) the following dimensionless
parameters are defined:
Input parameters of a numerical example may be:
.sigma..sub.o =1/1500 mm
R=10 meters
2.theta.=164.degree.
m=+1
.lambda..sub.1 =100 .ANG.
.lambda..sub.2 =200 .ANG.
w.sub.min =-25 mm
(W=50 mm)
w.sub.max =+25 mm
From equations 9-18, the resulting design parameters are determined
to be:
r=1011.488 mm
r'=964.542 mm
N.sub.2 =-1.63766 mm.sup.-2
N.sub.3 =+0.00267255 mm.sup.-3
Using these parameters, curves 200, 202 and 204 of FIG. 4 are the
individual optical aberrations calculated from equations 1 through
8 as functions of the selected wavelength. As constrained above,
the resolution is extremely high in the immediate vicinity of the
two chosen correction wavelengths (100 .ANG. and 200 .ANG.).
However, because equation 5 provides for the same optimum value of
N.sub.2 only for these discrete wavelengths, the image sharpness
degrades rapidly elsewhere. The result is a spectral resolution
which is generally as poor as the prior art design (Hettrick et al,
1986) employing an equally-spaced spherical grating (curves 100,
102 and 104) with the same groove density, angular deviation and
system length (r+r').
To overcome this limitation, a trick is employed which takes full
advantage of the fact that the grating grooves are unequally
spaced. At each wavelength other than the two chosen ones, the
grating is translated along its surface tangent. This effectively
changes the grating parameters as continuous functions of the
amount of translation .DELTA.w. Due to the large radius of
curvature R, the movement of the grating surface away from its
rotation axis is small [R(1-cos .phi.)] if the grating is
translated along the straight chord 40 fixed relative to the
grating surface (FIGS. 1, 3). Thus, in practice the grating
translation need not be constrained strictly along the curved
grating surface, greatly simplifying the mechanical design
(discussed below). From the geometry defined in FIG. 3, it follows
that equations 1-8 remain valid with the following
substitutions:
and where terms in the groove space variation (equation 2) higher
than N.sub.4 have not been retained. Note that .phi.=0 for a plane
grating.
Using the same numerical parameters previous given (and setting
N.sub.4 =0), curves 300, 302 and 304 of FIG. 4 are the calculated
results of optimizing .DELTA.w to eliminate defocusing at each
wavelength, by numerical iteration of equations (20) and (21) with
.phi. chosen such that F.sub.2 =0 from equation (5). All
wavelengths are now sharply in focus, the new limit to the optical
resolution being spherical aberration, which decreases as the third
power of the numerical aperture. It therefore has a resolvable
half-energy width approximately a factor of four smaller than the
extremum aberration plotted in FIG. 4C. The resulting spectral
resolution has thus improved approximately two orders of magnitude,
from 0.5 .ANG. (curve 200) to 0.003 .ANG. (curve 304 divided by
four).
Further correction is available by use of non-zero values for
N.sub.4. From equation (22) it is clear that this term will
significantly change the substituted value of N.sub.3 * as the
grating is translated (.DELTA.w.noteq.0). Through iteration of the
above numerical example, it was determined that a value of N.sub.4
=-6.99.times.10.sup.-7 mm.sup.-4 eliminates coma near the center of
the spectrum (curve 402), with the coma becoming in practice
negligible elsewhere compared to the spherical aberration (which
itself has been reduced in the process, as seen in curve 404). The
resulting symmetrical image allows the use of accurate modeling
techniques to further enhance the spectral resolution of a recorded
spectrum.
As plotted in FIG. 4D, only modest amounts of translation are
required, thereby allowing efficient use of the grating aperture
while maintaining a fixed beam direction. Furthermore, because this
motion functions to remove only a modest amount of residual
aberration the required accuracy of translation is trivial by
contemporary standards.
Due to the grating translation, an unbaffled grating will give rise
to an angular aperture whose center (or effective principal axis)
shifts by an equal amount. If this needs to be eliminated, then an
entrance baffle 50 (FIG. 1) may be inserted prior to the grating to
ensure underillumination. A translation of .DELTA.w combined with a
full grating ruled width of W, leads to a baffled grating width of
W-.DELTA.w. In the above numerical example, the assumed baffled
width of 50 mm and the translation of 25 mm requires a ruled
grating width of 75 mm. Thus, only a modest amount of the grating
is unused.
The small required grating size, modest translational travel,
undemanding translation accuracy and ability to use simple
rectilinear motion, leads to a simple and compact mechanical design
(FIG. 5), using commercially available components. Grating 12 is
contained in a holder 52 by use of set screws 54 which are
threadingly engaged in the holder. To prevent distortion of the
grating surface, set screws 54 may be spring-loaded ball plungers,
such as part no. 10001P manufactured by Northwestern Tools, Inc. of
Dayton, Ohio. The grating surface 14 is registered against pins 53
attached to the holder. By means of screws 56, holder 52 is rigidly
bolted to slide plate 58 which translates relative to end plates 60
and 82 by means of interposed inner ways 62 bolted to the slide
plate by screws 63, outer ways 64 bolted to the end plates by
screws 65, and ball or roller bearings 66. Thus, grating 12 is
allowed to translate along the direction 40 (normal to the plane of
FIG. 5) as illustrated in FIG. 1. Bearing assemblies consisting of
hardened ways and bearings are commercially available from numerous
sources, and need not be discussed further. The translation is
driven by a rotating cam 68 which is in surface contact with a
spherical ball 70 press fit into a bar 72 which is bolted to the
slide plate 58 by means of screws 76. This surface contact can be
assured by extension spring means 74 connecting the cam 68 and the
bar 72 by use of pins 76 attached to both members.
The grating rotation is also driven by a rotating cam 78 maintained
in surface contact with a ball 80 press-fit into a radius bar 82,
by spring and pin means 81 and 83, respectively, as detailed in
FIG. 6. Radius bar 82 also functions as one of the end plates as
discussed above. Both end plates 60 and 82 are supported by pivots
84 mounted by means of clamps 87 bolted to the stationary end
members 86 using screws 89. Similarly, clamps 61 provide mounting
of the opposite ends of pivots 84 onto end plates 60 and 82 by use
of screws 67. Hence, as bar 82 is pushed by cam 78, the end plates
60 and 82 co-rotate about pivots 84 together with the attached
grating 12. If pivot 84 is a flexural pivot, then spring 81 and
pins 83 are not required.
Support members 86 are affixed to a base plate 88 by means of bolts
90. Correlation of rotation between the cams 68 and 78 is
accomplished by mounting them to a common cam shaft 91 going
through their centers of rotation. The shaft is free to rotate
about is central axis by means of radial bearings 92. An
anti-backlash worm gear 93 is also rigidly attached (e.g. press-fit
or clamped) to shaft 91 and is driven by a worm 94 connected to a
drive shaft 95 which is free to rotate within radial/thrust
bearings 96 fit into base plate 88. Translation of worm 94 is
prevented by external retaining rings 97, one of which is supported
against leaf spring 98.
If external rotation means 99 is applied to drive shaft 96, both
the wavelength drive cam 78 and the grating translation cam 68 will
rotate synchronously. This provides for the automatic determination
of the amount of translation required at each wavelength. To obtain
the highest intrinsic mechanical accuracy, the wavelength cam may
have a circular surface and be rotated off of its geometrical
center, as illustrated in FIG. 6. Alternatively, the cam 78 may be
machined to a non-circular shape in accordance with providing a
linear relationship between the angle of cam rotation and the
selected wavelength. Due to the functional relationship shown in
FIG. 4D, as well as the correction necessary to remove the
translation of bar 72 due to rotation only of bar 82, the
translation cam is theoretically required to have a non-circular
shape. However only modest accuracy is required and therefore it
may be easily manufactured. The required accuracy may be easily
derived from FIGS. 4A and 4D, revealing a defocus of approximately
0.4 .ANG. per 25 mm of travel. Thus, even a 0.5 mm error in
translation would result in less than 0.01 .ANG. of residual
aberration.
Due to the translation of the varied space grating, the spacing at
pole 34 (FIG. 1) will change, and thus a conventional sine-bar
mechanism will not result in linearity between the angle of
rotation of a lead screw member (engaged to a normal pusher block)
and the resulting wavelength selected. However, as the dominant
change to the pole spacing is due to the N.sub.2 term [equations
(2) and (20)], such linearity can be regained to a high degree of
accuracy without resort to a cam, by use of an inclined plane as
the pusher block. FIG. 7 shows such an optional wavelength drive,
in which a lead screw 77 (which may be attached directly or
indirectly to drive shaft 95 of FIG. 5) is threadingly engaged into
a block 79 whose surface is inclined at an angle to the rotation of
the lead screw. In this configuration, a different bar 85 is
rigidly attached to slide plate 58 of FIG. 5 and is oriented along
the direction 40 of the grating translation. As the translation cam
moves this slide plate along the direction of its ways 62
(resulting in a change in the distance from ball 80 to the fixed
grating pole 34), the ball 80 attached to radius bar 85 will
migrate over the inclined plane pusher. This results in a built-in
mechanical correction to the grating angle in linear relationship
to the amount of grating translation, as required by the N.sub.2
term and the variation in incident angle given by equation (24).
For example, given the above numerical example, with N.sub.2
=-1.63766 mm.sup.-2, and a radius bar length of 556 mm, the pusher
block inclination angle would be 1.66.degree.. The residual
non-linearity is calculated to be approximately 0.3 .ANG..
In practice, external means 99 comprise various conventional gears,
bearings, cranks, motors, counters, etc. as convenient for the
particular application, and to enable accurate monitoring of the
grating position and orientation. In addition, as such a mechanism
may be used in combination with soft x-ray radiation, it would be
situated inside a vacuum, requiring use of conventional rotary
motion feedthroughs which are commercially available.
The mechanical couplings between the wavelength selection and
grating translation may of course be replaced by separate external
drives correlated by a computer.
The use of varied spaced grooves combined with suitable motions of
the grating surface as a function of wavelength, permits the
virtual elimination of significant optical aberrations in the
monochromatic image. Thus, linear dispersion becomes the limiting
factor in determining the attainable spectral resolution of such a
system. In the above numerical example, the spherical aberration
limit of 0.005 .ANG. will be reached only if the slits are
approximately 5 microns wide. This motivates the use of two (or
more) such systems in series, wherein the individual dispersions
add to increase the slit-limited resolution. In such
configurations, the exit slit for the first system is placed at the
same position as the entrance slit for the second system, and so
forth. The use of this intermediate slit is, however, optional, as
the additive dispersion will continue to disperse the various
wavelengths in a one-to-one mapping onto the final exit slit
plane.
Alternatively, the path length for all rays (principal and extrema)
may be made constant by use of two (or more) such systems arranged
such that the dispersions cancel. In this case, an intermediate
slit must be used to eliminate the background of overlapping
wavelength images. Such a (common path length) monochromator
preserves the time resolution of the incident beam, and is
therefore of interest in the context of pulsed sources.
While in the foregoing, a preferred embodiment of the present
invention has been set forth in detail for the purposes of making a
complete disclosure of the invention, it may be apparent to those
of skill in the art that numerous changes may be made in such
detail without departing from the spirit and principles of the
invention. In particular, optimizations other than equations 9-18
may be devised to minimize the required grating translation over
desired wavelength regions, or to eliminate aberrations at other
wavelengths.
A plane grating may also be substituted for the concave grating
illustrated above, in the case where both object and image are
real. In this case, there are insufficient degrees of freedom to
provide .DELTA.w=0 at two distinct wavelengths. The required amount
of translation necessary to provide in-focus imaging is therefore
larger than for the preferred embodiment. However one finds,
through use of equations 1-8 and 19-22 with an exceedingly large
value for R, that the required translation is minimized if a
maximum infinite de-magnification is chosen (i.e. the object is a
plane wave, and the image is diffracted into a negative spectral
order). Unfortunately, assuming the grating is baffled to maintain
a fixed direction for the principal ray, the larger translation
requires a correspondingly larger grating.
As another example, the same technique may used to dramatically
improve the properties of a plane grating having a virtual image
and real object [e.g. the erect field optical system of Hettrick et
al (U.S. Pat. No. 4,776,696)]. As with the concave grating
embodiment discussed above, the introduction of grating translation
in the latter design will also result in perfectly focused images
at all scanned wavelengths, thereby increasing the spectral
resolution. In this case, the amount of required translation is
very small, due to the fact that the erect field imaging is nearly
in focus prior to such translation. However, the improvement is
significant for high resolution applications.
As a further example of the versatility of the present invention,
the grating surface may be aspherical, which can be used to
self-focus in the direction parallel to the grooves without the
introduction of an additional mirror reflection.
While in the foregoing, embodiments of the present invention have
been set forth in considerable detail for the purpose of making a
complete disclosure of the invention, it may be apparent to those
of skill in the art that numerous changes may be made in such
detail without departing from the spirit and principles of the
invention.
In a fundamentally different application, the proposed translation
of a varied-space grating may be used by itself (i.e. without any
rotation required) to optimize the focusing of any varied-space
grating. For example, this method may be used to optimize the
resolution of a spectrum recorded by the prior art gratings of
Hettrick et al (1983), Hettrick et al (U.S. Pat. No. 4,776,696),
Harada et al (U.S. Pat. No. 4,312,569), Harada et al (1984), or
Meekins et al (U.S. Pat. No. 4,578,804).
Finally, it should be recognized that while the invention has been
applied in detail to electromagnetic radiation, it may be utilized
in principle with wavelike radiation of any nature, including
acoustic waves.
* * * * *